Re: An uncountable countable set

Virgil wrote:
In article <45287609@xxxxxxxxxxxxxxxxxxx>,
Tony Orlow <tony@xxxxxxxxxxxxx> wrote:

Mike Kelly wrote:

They have to be infinitely close, so actually, they have an
infinitesimal segment between them. :)
And what the *** does "infinitely close" mean, anyway?

Less than any finite distance. Silly!

Zero is a finite distance, so it is TO who is being silly.

If the distance between two points is 0, there is only one point.


Besides which, infinitesimal segments, if they exist at all, are infinitely bisectable.

You will not find any new standard reals in that interval besides the one which is equal to the points at both ends. ANy two standard reals have a finite difference. That's why you can find another between them.
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